Topics in Hydrodynamics (Mathematics)

9353093 弗里德兰德博士最近的研究涉及与流体力学方程（欧拉方程和纳维尔-斯托克斯方程）和磁流体力学方程的扩展系统有关的某些问题。 所采用的数学包括偏微分方程，渐近方法和动力系统的技术。 所研究的问题是 由地球物理学和天体物理学流体动力学中出现的问题激发。 这项研究项目将涉及与M. M.维希克 弗里德兰德博士将继续对这些问题的几个方面进行调查。 本文的研究分为四个部分：（I）“快速”发电机问题;（II）欧拉方程的不稳定性判据;（III）流体动力学时间周期中Floquet根向量的完整系统的存在性;（IV）磁流体动力学稳定性。 在东道机构开展的互动活动包括：（1）讲授关于流体动力学数学专题的研究生课程;（2）为数学科学领域的女学生和博士后提供指导和咨询;（3）组织为期两天的研讨会式讲习班，由杰出女数学家主讲。 该项目进一步推动了自愿工作妇女方案的目标，即：（1）为妇女提供机会，使她们在工程和国家科学基金会支持的科学学科中取得职业发展;（2）通过提高在工业、政府和学术机构就业的女科学家和工程师的知名度，鼓励妇女从事科学和工程职业。 通过鼓励妇女参与科学，这是对国家未来的宝贵投资。 ***

9353093 Friedlander Dr. Friedlander's recent research involves the study of certain problems related to the equation of hydrodynamics (the Euler equations and the Navier-Strokes equations) and to the extended system of the equations of magnetohydrodynamics. The mathematics employed includes techniques from partial differential equations, asymptotic methods and dynamical systems. The problems studied are motivated by questions that arise in geophysical and astrophysical fluid dynamics. This research project will involve joint work with M.M. Vishik. Dr. Friedlander will continue her investigation of several facets of these problems. The research is described under four headings: (I) The "fast" dynamo problem; (II) Instability criteria for the Euler equations; (III) The existence of a complete system of Floquet root vectors in time periodic of fluid dynamics; (IV) Magnetohydrodynamic stability. Interactive activities at the host institution include: (1) teaching a graduate course on mathematical topics in fluid dynamics; (2) mentoring and counseling women students and postdocs in the mathematical sciences; and (3) organizing a two-day workshop of colloquium style lectures given by distinguished women mathematicians. This project furthers VPW program objectives which are (1) to provide opportunities for women to advance their careers in engineering and in the disciplines of science supported by NSF and (2) to encourage women to pursue careers in science and engineering by providing greater visibility for women scientists and engineers employed in industry, government, and academic institutions. By encouraging the participation of women in science, it is a valuable investment in the Nation's future significantly. ***